Method of modeling the socio-spatial dynamics of extreme urban heat events

ABSTRACT

A method of coupling surface urban heat island measures with socio-economic indicators of vulnerability to create improved spatially specific models to assist public health professionals in predicting extreme heat events mortality in urban environments. The method includes utilizing landsat TM imagery for the measuring of the urban heat island intensity levels and a spatial analysis of the variables in question.

GRANT STATEMENT

This invention technology was made with government support under Contract No. 200-2006-15969 from the Center for Disease Control (CDC). The Government has certain rights to this invention.

TECHNICAL FIELD OF THE INVENTION

The present invention relates generally to the field of mathematics, and, more particularly, to the mathematical modeling of the interaction of society and environmental events.

BACKGROUND OF THE INVENTION

Extreme heat is a prolific weather-related killer in the United States as well as the rest of the world. Notable extreme heat events (EHE's) within the last two decades include a seven day period in Philadelphia, Pa., in July of 1993 accounting for 118 deaths and a less than seven day period Chicago, Ill., in July of 1995 accounting for 700 deaths. Outside of North America, France experienced an EHE in the summer of 2003 that accounted over tens of thousands of deaths. Thus, heat-related morbidity and mortality are among the primary health concerns expected to increase as a function of climate change.

There is significant disparity in the populations involved in heat-related morbidity/mortality. Generally, various social characteristics have been associated with urban disasters. Those sufferers of poverty, those with poor education, those designated by minority status, the very young, and the elderly are groups identified as disproportionally impacted by urban disasters. However, the distribution of vulnerability to EHEs among the various groups, as defined by the social characteristics listed above and various combinations of the same, is largely unknown. Furthermore, the interaction between the various social characteristics and EHEs is not simple, and is further exacerbated by built (urban) environments.

The urban heat island (UHI) effect, a function of the urban environment, is defined as the temperature differential between the contiguous rural area and its related urbanized space. The UHI effect likely serves to magnify the lethality of EHEs. The effect, however, is not a straight forward and simple magnification. The UHI effect is complex and dependent upon a number of factors. The UHI effect stems from the lack of vegetation, low thermal conductivity and/or high heat capacity materials used in the built environment, and the urban canyon-like geometry. UHIs are typically spatially heterogeneous, with differing levels of heat intensity occurring within a city (aka micro-UHIs). Vulnerable groups spatially coincident with these micro-UHIs are thought to be at an even greater increased risk of heat-related mortality.

The spatial analysis of vulnerability, linking social and built environment variables to EHEs within urban areas, is limited. Investigators have demonstrated that warmer and more socially disadvantaged areas are more prone to heat-related deaths. But investigators have undertaken no direct physical measure of temperature. Furthermore, there has been no adequate measure of heat load or of the socioeconomic disadvantages of a given neighborhood in relation to UHI's or EHE's.

Previous approaches utilizing the Human Thermal Comfort Index (HTCI) suffer from a similar problem. While indicating a strong positive spatial relationship between heat stress and the percentage of poverty and minority, these approaches suffer from using estimated UHIs as well as from a lack of a direct accounting for socioeconomic factors. In essence, previous approaches fail in as far as they does not provide a true or useful mechanism with which to predict where the greatest concentrations of mortality and morbidity will occur within an urban environment during an EHE.

Cities are facing ever greater financial constraints upon their abilities to respond to social and environmental harms. Additionally, it is expected that EHEs will likely increase both in duration and intensity as a result of climate transformation. Taken together, these elements indicate a scenario that underscores the need to further understand the phenomena of extreme heat, identify at-risk populations and mitigate effects and impacts upon those populations. Cities must be able to better predict where their EHE response mechanisms must be concentrated to most effectively combat the mortality and morbidity caused by future EHEs. The enhanced ability to delineate the risk of morbidity and mortality at finer scales within urban environments will enable better and more cost effective concentration of mitigation efforts and preventative measures yielding improved medical and preventative responses and superior post EHE recovery.

Thus there remains a need for an improved, spatially specific method to identify populations at risk from EHE's. The present novel technology addresses this need.

SUMMARY OF THE INVENTION

The urban heat island effect during extreme heat events is coupled with socioeconomic indicators of vulnerability to enable the development of mortality and morbidity risk models with improved spatial specificity. Model development data is derived from reported urban mortality and morbidity values during an extreme heat event. Socioeconomic characteristics believed to be of importance are taken from existing studies on the vulnerability of populations to extreme heat. The urban heat island effect is mapped and broken into intensity levels over the area in question during the extreme heat event. A spatial analysis is performed determining the relative importance of any given socioeconomic characteristic in predicting the sensitivity of its representative sub population to an extreme heat effect under an urban heat island effect. A model utilizing the importance weighted socioeconomic characteristics and heat intensity levels as independent variables to predict the spatial distributions of extreme heat event mortality is created. One object of the present novel technology is to enhance the spatial specificity of extreme heat event mortality predictions to assist public health professionals. Other objects and advantages will become apparent from the following description.

DETAILED DESCRIPTION

For the purposes of promoting an understanding of the principles of the invention and presenting its currently understood best mode of operation, reference will now be made to the embodiments illustrated and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended, with such alterations and further modifications in the illustrated device and such further applications of the principles of the invention as illustrated therein being contemplated as would normally occur to one skilled in the art to which the invention relates.

The present novel technology was developed to improve urban response to EHE's. Consequently, the following examples and embodiments to reflect and reference a study area consisting of a large, urban area. This study environment was selected such that the large, urban area has experienced an extreme heat event. Furthermore, this particular urban area was selected in part because for the time of the extreme heat event there was available associated population data and landsat TM imagery data. As such, EHE's are naturally occurring and infrequent, and not inherently reproducible in a controlled laboratory environment, this study is frequently referenced herein. However, it should be kept in mind that the present novel technology is broadly applicable beyond the specific details and characteristics of the study embodiment referenced herein.

Vulnerable Populations

Census data are derived at the block group level following the socio-economic characteristics of vulnerability (such as: Hispanic population, black population, Asian population, Native American population, Other race population, Age 65 and over, age 65 and living below poverty, age 5 and under, population living below poverty, low education, and the like) to extreme heat. Estimates of population are derived by normalizing the total population by the area of residential land use within each block group. The area of residential land use within a block group may be determined through any number of methods including satellite imagery, aerial survey, and the like. The area of residential land use is typically selected over other possible values, such as total block group area, because it provides a truer indicator of residential density within each block group. This is to say that it provides a more accurate description of the residential density within each block group. However, any convenient relevant value may be chosen

Decedent Mapping

Heat related fatalities for the area in question is obtained. The data is typically filtered to only include those deaths that occurred during the previously mentioned extreme heat event. The addresses of those qualified decedents are then assigned geographic identifies (hereafter geocoded). Additionally, the deaths within each block group are totaled to produce a dataset representative of block group level EHE mortality.

Urban Heat Island Mapping

Typically, the Landsat thermal mapping (hereafter TM) imagery is acquired for the time period in question. The thermal band of the image is then converted to an at-satellite brightness temperature per the following equation,

$T = \frac{K\; 2}{\ln\left( {\frac{K\; 1}{LW} + 1} \right)}$

where T is an estimate of land surface temperature in Kelvin. K2 is the calibration constant for temperature in Kelvin and K1 is the constant for radiance in mWcm^(2μm) ⁻¹. L_(w) is the spectral radiance in mWcm², calculated from the digital number values of the landsat TM thermal band.

Typically, T is then averaged by block group. This is done to determine the mean estimated land surface temperature per block group. The average T values are then uniformly stratified into the number of different levels desired.

Spatial Analysis

The typical spatial analysis method is the standard deviational ellipse (SDE). It is a well known method and highly suited for point patterns. The end result of this analysis is the assignment of a weight to each of the descriptive variables. For example, in the most simple case, the variables found to be highly descriptive of the data are assigned a weight of 1 (one) while those not found so are assigned a weight of 0 (zero).

The calculation of the SDE is reasonably uncomplicated and many current GIS applications allow for its use. The SDE first requires that the centroid of each block group be calculated and the demographic measures, decedents and T measures respectively be assigned. Typically, a weighted mean center of the point set will also be calculated as part of the calculation of the SDE. Use of the weighted mean center provides a better descriptor of vulnerability than a non-weighted mean center. The weighted mean center is obtained by averaging the coordinates of all the points and providing a weight to each based on an attribute variable of interest. After the mean center is calculated, each point is then transformed into a different metric space referenced from the mean center. The equation for this transformation is X′_(j)=X_(j)−X_(weighted mean center) with the Y transformation essentially being the same equation. The angle of rotation from the transformed points is calculated by

${\tan \; \theta} = {\begin{pmatrix} {{\sum\limits_{i - 1}^{n}\; X_{i}^{\prime 2}} -} \\ {\sum\limits_{i - 1}^{n}\; Y_{i}^{\prime 2}} \end{pmatrix} + {\sqrt{\begin{pmatrix} {{\sum\limits_{i - 1}^{n}\; X_{i}^{\prime 2}} -} \\ {\sum\limits_{i - 1}^{n}\; Y_{i}^{\prime 2}} \end{pmatrix} + 4}\frac{\left( {\sum\limits_{i - 1}^{n}\; {X_{i}^{\prime}\; Y_{i}^{\prime}}} \right)^{2}}{2{\sum\limits_{i - 1}^{n}\; {X_{i}^{\prime}\; Y_{i}^{\prime}}}}}}$

The standard distance on X and Y are then calculated as

δ_(X)=√{square root over ((Σ_(i−1) ^(n)(X′ _(i) cos θ−Y′ _(i)sin θ))² /n)}

δ_(Y)=√{square root over ((Σ_(i−1) ^(n)(X′ _(i) sin θ−Y′ _(i)cos θ))² /n)}

θ_(X), θ_(Y), X_(weighted mean center), Y_(weighted mean center), and area are used to quantitatively compare the spatial distributions of all the variables. Standard T-test and F test are used to determine the levels of spatial similarity. This in turn indicates the importance of the actual variables when describing the real data.

Additional evaluations of the variables and their importance in describing the data are achieved through evaluation of concentration and eccentricity. A death concentration value is calculated within the spatial distributions of T. Eccentricity values are calculated as θ_(X)/θ_(Y). The concentration value describes the level of concentration of the spatial phenomena and the eccentricity indicates the polarity of the point distribution within the ellipse. With respect to a variable, the greater the concentration of death and/or smaller eccentricity, the greater coverage of that variable's descriptive capability with respect to the actual data.

Modeling

Typically, a multiple regression modeling technique is used. First, all non-zero weighted variables are interpolated to standard sized cells covering the study area using a kernel density function. After calculation of the kernel density, the mean value per block group residential area is calculated. The non-zero weighted variables are evaluated for multi-collinearity. If needed, any collinearity is removed. A mapping of the kernel density of real death points (the actual data) is performed.

A multiple regression utilizing the non-zero weighted variables and T as the independent variables is performed, with density of EHE death being the dependent variable. Outputs of the regression are generated, forming standardized predictive values of risk. These values are mapped at the census-block group level with decedent locations as the validation layer. The standard R² test (a test that determines what fraction of the total squared error is attributed to the model) or the like may be used to determine the effectiveness of the model in explaining the variation of the dependent variable.

Following a significant R² value, the models outputs can be viewed as spatially predictive values of future risk. Maps depicting spatial variation of risk, typically through a 3-D map with the Y axis representative of relative risk or the like of the city can be created. In the event of an extreme heat event or a predicted extreme heat event, health care professionals concentrate intervention measures into areas denoted as at high risk.

While the invention has been illustrated and described in detail in the foregoing description, the same is to be considered as illustrative and not restrictive in character. It is understood that the embodiments have been shown and described in the foregoing specification in satisfaction of the best mode and enablement requirements. It is understood that one of ordinary skill in the art could readily make a nigh-infinite number of insubstantial changes and modifications to the above-described embodiments and that it would be impractical to attempt to describe all such embodiment variations in the present specification. Accordingly, it is understood that all changes and modifications that come within the spirit of the invention are desired to be protected. 

1. A method for creating a risk model for determining the spatial specificity of the most at-risk subpopulations from an extreme heat event within an urban setting, comprising: (a) generating a data set at the block group level from census data, wherein a block group represents an area-standardized partition on a grid map of an urban setting and wherein the data set further comprises groupings of population apportioned according to a plurality of predetermined vulnerability characteristics; (b) generating estimates of population density data at the block group level; (c) generating heat-related decedent data; (d) generating urban heat island intensity level data; (e) generating lists of the significant socio-economic variables of vulnerability and of the significant urban heat island intensity levels from the data set at the block group level and the estimated population density at the block group level and the heat-related decedent data and the urban heat island intensity levels; (f) generating a predictive vulnerability assessment model using the significant social economic variables of vulnerability and the significant urban heat island intensity levels and the heat-related decedent data; and (g) allocating city resources according to the predictive vulnerability assessment model in response to an extreme heat event event.
 2. The method of claim 1 and further comprising: (h) after (a) and before (b), further categorizing the census data into social vulnerability sub-categories.
 3. The method claim 1 wherein (b) further comprises normalizing the total population by the area of residential land use within each block group.
 4. The method claim 1 wherein the heat-related decedent data is confined to previous extreme heat events.
 5. The method of claim 1 and wherein the block groups are assigned a stratified urban heat island intensity level.
 6. The method of claim 1 and further comprising: (i) after (e) and before (f), assigning significance weight to the social vulnerability sub-categories wherein the significance weight is representative of the spatial similarity of the social vulnerability sub-category to the extreme heat event heat-related decedent data.
 7. The method of claim 1 and further comprising: (j) after (e) and before (f), creating a continuous kernel density surface of the significant social economic variables of vulnerability and the significant urban heat island intensity levels.
 8. The method of claim 1 and further comprising: (k) creating a continuous kernel density surface of the heat-related decedent data.
 9. The method of claim 1 and further comprising: (l) calculating the mean value per block group residential area of the continuous kernel density surface.
 10. The method of claim 1 wherein the vulnerability assessment model is generated through a regression analysis using the mean value of the continuous kernel density surface per block group residential area, T and the significance weighted social vulnerability subcategories as the independent variables and the density of extreme heat event mortality as the dependent variable.
 11. The method of claim 1 wherein the output of the vulnerability assessment model is validated against a density surface of actual extreme heat event mortality.
 12. The method of claim 1 wherein the predictive vulnerability assessment model is then used to color code a map denoting the areas of predicted greatest extreme heat event mortality for various combinations of the significant urban heat island intensity levels and significant social economic variables of vulnerability.
 13. A method for determining the significance of a social economic variable of vulnerability within the context of a urban heat island effect, with respect to urban extreme heat event mortalities comprising: (a) calculating the centroid of each plurality of block group, wherein each respective block group represents an equal portion of the area on a grid map of an urban setting; (b) assigning measures of socio-economic vulnerability, decedents, and stratified temperature to the centroid; (c) calculating a weighted mean center of extreme heat event mortalities; (d) calculating weighted mean centers of socio-economic variables of vulnerability using the respective centroids as points; (e) calculating a weighted mean center of stratified temperatures using the respective centroids as points; (f) calculating an EHE standard deviation ellipse of the extreme heat event mortalities, using the weighted mean center as the origin; (g) calculating an eccentricity value for the EHE standard deviation ellipse of the extreme heat event mortalities; (h) calculating a respective standard deviation ellipse for each socio-economic variable; (i) calculating a respective standard deviation ellipse for each stratified temperature value using the corresponding weighted mean center; (j) using T-test and F-test techniques to determine spatial similarity between the respective EHE standard deviation ellipses and the respective standard deviation ellipses for each socio-economic variable and for each stratified temperature value; (k) calculating an extreme heat event mortality concentration within each standard deviation ellipse for each socio-economic variable and for each respective stratified temperature value shown to be spatially similar as the number of extreme heat event mortalities coincident within the standard deviation ellipse divided by the area of the standard deviation ellipse; (l) calculating the eccentricity for each respective socio-economic variable and for each respective stratified temperature value identified to be spatially similar; (m) marking each identified spatially similar socio-economic variable and stratified temperature value significant where the extreme heat event mortality concentration is above a predetermined threshold and the eccentricity value is within a predetermined range of the eccentricity of the extreme heat event mortality; and (n) providing an output of the significant socio-economic variables and stratified temperature values.
 14. The method of claim 13 and further comprising; using the output of a method for creating a risk model for determining the spatial specificity of the most at-risk subpopulations from an extreme heat event within an urban setting.
 15. The method of claim 14 and further comprising; (a) a method for creating a risk model for determining the spatial specificity of the most at-risk subpopulations from an extreme heat event within an urban setting, comprising: (b) generating a data set at the block group level from census data, wherein a block group represents an area standardized partition on a grid map of an urban setting and wherein the data set further comprises groupings of population apportioned according to a plurality of predetermined vulnerability characteristics; (c) generating estimates of population density data at the block group level; (d) generating heat-related decedent data; (e) generating urban heat island intensity level data; (f) generating lists of the significant socio-economic variables of vulnerability and of the significant urban heat island intensity levels from the data set at the block group level and the estimated population density at the block group level and the heat-related decedent data and the urban heat island intensity levels; (g) generating a predictive vulnerability assessment model using the significant social economic variables of vulnerability and the significant urban heat island intensity levels and the heat-related decedent data; and (h) allocating city resources according to the predictive vulnerability assessment model in response to an extreme heat event.
 16. A method for creating a predictive model for the spatial concentrations of extreme heat event mortality within an urban setting utilizing socio-economic indicators of vulnerability and stratified urban heat island effects, comprising: (a) allocating census data to a plurality of block groups, wherein each respective block group represents an equal area on a grid map of an urban setting and wherein allocation of census data further comprises differentiation of population according to a plurality of predetermined vulnerability characteristics; (b) calculating estimates of population density at the block group level; (c) counting the number of heat-related decedents; (d) measuring urban heat island intensity levels; (e) stratifying the measured urban heat island intensity values; (f) designating significant socio-economic variables of vulnerability and the significant urban heat island intensity levels from the allocated and differentiated census data set at the block group level and the estimated population densities and the number of heat-related decedents and the urban heat island intensity levels; (g) creating a predictive model for the spatial concentrations of extreme heat event mortality in an urban environment using the designated significant social economic variables of vulnerability and the significant urban heat island intensity levels and the heat-related decedent data; and (h) distributing city resources according to the predictive model for the spatial concentrations of extreme heat event mortality in an urban environment in response to an extreme heat event.
 17. The method claim 16 wherein (c) further comprises normalizing the total population by the area of residential land use within each block group.
 18. The method claim 16 wherein the heat-related decedents are confined to previous extreme heat events.
 19. The method of claim 16 and wherein the block groups are assigned a stratified urban heat island intensity level.
 20. The method of claim 16 and further comprising: (i) after (f) and before (g), assigning significance weight to the social vulnerability sub-categories wherein the significance weight is representative of the spatial similarity of the social vulnerability sub-category to the extreme heat event heat-related decedent data.
 21. The method of claim 16 and further comprising: (j) after (f) and before (g), creating a continuous kernel density surface of the significant social economic variables of vulnerability and the significant urban heat island intensity levels.
 22. The method of claim 16 and further comprising: (k) creating a continuous kernel density surface of the heat-related decedent data.
 23. The method of claim 16 and further comprising: (l) calculating the mean value per block group residential area of the continuous kernel density surface.
 24. The method of claim 16 wherein the predictive model for the spatial concentrations of extreme heat event mortality in an urban environment is generated through a regression analysis using the mean value of the continuous kernel density surface per block group residential area, the stratified heat intensity levels and the significance weighted social vulnerability subcategories as the independent variables and the density of extreme heat event mortality as the dependent variable.
 25. The method of claim 16 wherein the output of the vulnerability assessment model is validated against a density surface of actual extreme heat event mortality.
 26. The method of claim 16 wherein the predictive vulnerability assessment model is then used to color code a map denoting the areas of predicted greatest extreme heat event mortality for various combinations of the significant urban heat island intensity levels and significant social economic variables of vulnerability. 